In this example, we will design an integrated biosensor circuit and calculate its sensitivity to small refractive index changes due to the presence of an analyte on a waveguide.
Waveguide design
We want to design a silicon on insulator (SOI) waveguide for operation in water with an evanescent field that extends approximately 30nm above the waveguide because the analyte will bind to the top surface of the waveguide and modify the refractive index for approximately 30nm. For this, we choose the fundamental TM mode of an SOI waveguide that is 220nm high and 800nm wide. This waveguide supports 3 guided modes: 2 TE-like modes and 1 TM-like mode. Please note that in the file biosensor_waveguide.lms symmetric boundary conditions are used so the fundamental TE mode will not be found. To see all 3 guided modes, the symmetric boundaries can be removed.
The waveguide is constructed in biosensor_waveguide.lms, and the fundamental TM mode at 1550nm is shown below. We can see that the TM mode is a good choice because the electric field is very intense precisely where the analyte will be bound to the waveguide surface.
We then use a parameter sweep to vary the analyte refractive index from the background (n=1.33) to n=1.34. The analyte is assumed to be a rectangular region that extends 30nm above the waveguide top surface. We can easily visualize the effective index of the waveguide as a function of analyte index.
We can export the change in effective index to a text file, called delta_neff_vs_index.txt, that can be used by INTERCONNECT with the following lines of script
nTM = getsweepresult("neff","neff_2"); # use "neff_3" if symmetry is disabled
index = nTM.index;
nTM = nTM.neff;
delta_nTM = nTM-nTM(1);
# export the TM data to file
outdata = [ pinch(index), real(delta_nTM), imag(delta_nTM) ];
format long;
filename = "delta_neff_vs_index.txt";
if(fileexists("filename")) { rm(filename); }
write(filename,num2str(outdata));
If we want to calculate the temperature dependence of the effective index, we can change the silicon material to be "Si with T dependence" and the glass to be "SiO2 with T dependence". These are analytic materials where the refractive index is set to be n(1550nm) + dn/dT*x1. For Si we use dn/dT = 1.9e-4 while for glass we use 8.5e-6 which are approximately the thermo-optical coefficients at 1550nm and 295K. The variable x1 represents T = (T-295K). After running the script file T_dependence_calc.lsf, we obtain a temperature dependence shown below. This script also outputs a file called delta_neff_vs_dT.txt for later use in INTERCONNECT.
After calculating the temperature dependence at 1550nm, we should return to using the original dispersive materials ("SiO2 (Glass) - Palik" and "Si (Silicon) - Palik") and this is done automatically at the end of the script T_dependence_calc.lsf. We then calculate the mode at 1500nm and perform a frequency sweep from 1500nm to 1600nm while tracking the TM mode. As shown below, we should check the "detailed dispersion calculation" check box as well as the "store mode profiles while tracking" check box since these are required for export to INTERCONNECT.
Once complete, we can export the MODE information for INTERCONNECT by setting the options pull down to "Data export" and pressing the "Export for INTERCONNECT" button.
When exporting, choose the file name mode_file_biosensor.ldf. If the file exists, choose to overwrite it. You will then see the window below. Set the Label to TM and the Orthogonal ID to 1. The Orthogonal ID is used by INTERCONNECT to uniquely identify modes and it is important that this value be set correctly.
We are now ready to proceed to the circuit simulation
Circuit simulation
Open the file biosensor_circuit.icp. The circuit is shown below. This circuit contains a basic Mach-Zehnder setup. The arms of the interferometer are different lengths: the reference arm is only 100 microns long, while the sensing arm is 1mm long. Note that in practice this longer arm could be a tightly wrapped waveguide to minimize the total sensing area. In addition, for the purposes of simulation, we have also introduced an optical phase shifter. This phase shifter is typically used for elecro-optical modulators and it adds a small shift in effective index (and loss) that depends on an input voltage. Rather than an input voltage, here we are using the analyte index as the input and it will vary from 1.33 to 1.34. We add a second phase shifter element which represents the phase shift due to temperature changes. In this manner we can independently control these effects.
The basic waveguides are mode waveguides, with mode profile, effective index, group index and dispersion imported from the frequency sweep file we created in the previous step with MODE. The text file that determines the change in effective index as a function of analyte refractive index was also created in the previous step and is imported into the phase shifter.
In addition, we use S parameter objects to represent grating couplers. The S parameters for these calculations are taken from the 2D grating couplers simulations at Grating Coupler 2D-FDTD.
The FSR of an ideal Mach-Zehnder is given by
$$ F S R=\frac{c}{n_{g}\left(L_{2}-L_{1}\right)} $$
where L1 and L2 are the lengths of the 2 arms and ng is the group index of the waveguide.
The change in analyte index required for a 2π phase change in the second arm is
$$ \Delta n_{\text {analyte}}=\frac{\lambda_{0}}{L_{2}} \frac{\partial n_{\text {analyte}}}{\partial n_{e f f}} $$
and the change in temperature required for a 2π phase change in the second arm is
$$ \Delta T=\frac{\lambda_{0}}{L_{2}} \frac{\partial T}{\partial n_{e f f}} $$
With our design, and the choice of 100microns and 1mm respectively for L1 and L2, we have: FSR ~ 83GHz, nanalyte ~ 0.012, T ~ 11 degrees.
The circuit schmatic is shown below.
Result
We can run this simulation by pressing the run button. Once complete, which takes only about a second, we can visualize the transmission of the TM mode, remembering to plot the absolute value squared of this result. We can then switch back to layout mode, adjust the analyte refractive index to 1.336 and repeat. We choose the value of 1.336 because it is 1.33+0.012/2 and therefore we expect it to shift the phase of the second arm by π. If we visualize in the same visualizer, we will see the figure below. We see that the FSR is close to the expected value and that we obtained the expected π phase shift. Please note that this result is shown without the grating couplers included.
If we include the grating couplers, we see the following result.
The effect of the grating couplers is mainly to reduce the overall transmission. It also introduces some reflection which is shown below.
To determine the maximum sensitivity of the device, we perform a parameter sweep of the index from 1.33 to 1.336. We will record the transmission and we will also record the value of the transmission at the center frequency. The figure below shows the absolute value squared of the transmission as a function of frequency and index.
More importantly, we can plot the absolute value squared of the transmission at the center frequency, which is what an integrated photodiode would measure if a cw laser were used as a source. We see this result in the figure below.
If we operate at the most sensitive operating point (where the slope is most steep) the slope is approximately 67 / RIU. If we assume that our detector is sensitive to changes of approximately 1/1000th of the dynamic range (a transmission of 0 to 0.25), then we can measure index changes of a 1e-3 / 0.25 / (67/RIU) = 6e-5 RIU. Therefore this system could detect a change in refractive index in the 30nm above the waveguide surface of 6e-5. The sensitivity could be increased by increasing the length of the second arm but this can also cause additional problems with thermal stability.
Building an integrated sensor
To build an integrated sensor, we would need a grating coupler to bring light from an external CW laser onto the chip through a fiber. The Mach-Zehnder output would need to be fed into an integrated photodector. An electronically controlled heater would need to heat the sensing arm up and down to find the desired operating point - where the detector is operating at about 1/2 its maximum value - and to maintain a stable temperature. As the analyte binds to the surface of the waveguide, the detector response will increase or decrease, and the change in output intensity can be calibrated to measure the change in refractive index above the waveguide and therefore the concentration of analyte. The photodiode readout must be able to measure changes of 1/1000th of the dynamic range.
The challenges with building this devices are
- Maintaining thermal stability
- The chemistry required to functionalize the waveguide surface
- The existence of two TE modes in the waveguide which can lead to increased noise. The splitters and waveguide bends can couple the TM and TE modes, leading to increased noise.
The issues of thermal stability and the multi-mode waveguide behavior could be further investigated with INTERCONNECT.